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In a large cohort of such women, there was a slight increase in the number of stillbirths and a doubling in the expected incidence of mental retardation and nonfebrile seizures in their offspring Issues regarding a coagulopathy in the fetus exposed to phenobarbital and certain of the other drugs are well known to obstetricians and pediatric specialists and are treated with the oral ad-.

Figure 31-16. Bilateral acoustic schwannomas in neuro bromatosis type 2. MRI in the axial plane, without (left) and with (right) enhancement.

Figure 34-27. Cerebral angiogram of a cerebral dural arteriovenous malformation. The nidus is located at the cerebral convexity (arrow). There is rapid ling of the cerebral venous system after injection of dye into one internal carotid artery.

2x 1 x 8 , then x 5 7x p p 2 619 7 2449 b x a x 15 30 4 c x 2 only d x 2; 3 A mixture containing 16% of a drug is to be combined with another mixture containing 28% of a drug to obtain 15 ml of a 24% mixture. How much 16% mixture is required If (a) 5 ml (b) 7 ml 4 . 2 x b 2 x c 2 4 x d Cannot be reduced (c) 10 ml (d) 12 ml

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Question 26-7

a1 a1 + a2 a3 or a1 + a2 a2 a3 b1 + b2 b2 b3 c1 + c2 c2 c3 d1 + d2 d2 d3 b1 b1 + b2 b3 c1 c1 + c2 c3 d1 d1 + d2 d3

Subacute Necrotizing Encephalomyelopathy (Leigh Disease; SNE)

11 Show that in any base b 2, the sum of any three single-digit numbers is at most two digits long 12 Show that any binary integer is at most four times as long as the corresponding decimal integer For very large numbers, what is the ratio of these two lengths, approximately 13 A d-ary tree is a rooted tree in which each node has at most d children Show that any d-ary tree with n nodes must have a depth of (log n/ log d) Can you give a precise formula for the minimum depth it could possibly have 14 Show that log(n!) = (n log n) (Hint: To show an upper bound, compare n! with nn To show a lower bound, compare it with (n/2)n/2 ) 15 Unlike a decreasing geometric series, the sum of the harmonic series 1, 1/2, 1/3, 1/4, 1/5, .

diverges; that is, 1 = i i=1 It turns out that, for large n, the sum of the rst n terms of this series can be well approximated as n 1 ln n + , i i=1 where ln is natural logarithm (log base e = 2718 ) and is a particular constant 057721 . Show that n 1 = (log n) i i=1 (Hint: To show an upper bound, decrease each denominator to the next power of two For a lower bound, increase each denominator to the next power of 2) 16 Prove that the grade-school multiplication algorithm (page 21), when applied to binary numbers, always gives the right answer 17 How long does the recursive multiplication algorithm (page 22) take to multiply an n-bit number by an m-bit number Justify your answer 18.

Justify the correctness of the recursive division algorithm given in page 23, and show that it takes time O(n2 ) on n-bit inputs 19 Starting from the de nition of x y mod N (namely, that N divides x y), justify the substitution rule x x mod N, y y mod N x + y x + y mod N, and also the corresponding rule for multiplication 110 Show that if a b (mod N ) and if M divides N then a b (mod M ) 112 What is 22 111 Is 41536 94824 divisible by 35.

The common log of 1,000 is 3, because 103 = 1,000. The common log of 10,000 is 4, because 104 = 10,000. As a number gets larger without limit, so does its common log. The size of the logarithm grows much more slowly than the size of the number.

The McGraw Hill Companies, 2010

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